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Wacky
Water World: Teacher Notes
MA.912.A.3.8
MA.912.A.3.11
MA.912.A.3.13
MA.912.A.3.15
Conceptual Knowledge
Linear Equations
Graphing Calculators
Interpret Data
Procedural Knowledge
y = mx + b
Graphing Linear Equations
Graphing Calculator Commands
Make Predictions
Problem Solving
Reasoning
Communication
Connections
Representation
It is Saturday and the
new water theme park has just opened. You and your friends are making
plans to attend. You check the plans at the ticket counter, and since
you have a limited amount of money, you want the best buy.
Students work individually
or in pairs
Graphing Calculator
Study the two plans below
and then decide which plan you will recommend to your friends.
| Plan A |
Plan B |
| $ 5.00
admission |
$ 10.00
admission |
| $ 1.00
per ride |
$ .50
per ride |
Which plan will you recommend?
___________
Why? (be specific and write complete sentences)
____________________________________________________________________________
____________________________________________________________________________
____________________________________________________________________________
Calculate the total cost under both plans for riding 0, 1,
2, 3, 4, 5, and 6 rides. Do this without a calculator.
|
Plan
A
|
Plan
B
|
|
Rides
|
Total
Cost
|
Rides
|
Total
Cost
|
|
0
|
|
0
|
|
|
1
|
|
1
|
|
|
2
|
|
2
|
|
|
3
|
|
3
|
|
|
4
|
|
4
|
|
|
5
|
|
5
|
|
|
6
|
|
6
|
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Describe how to find the total
cost of going under Plan A and riding any number of rides.
The total cost will equal _____ plus _____ times the number of rides.
Describe how to find the cost using symbols only!
Use Y to equal the total cost and X to equal the
number of rides.
Y
= _____ + _____X
Describe how to find the total cost of going under Plan B and riding
any number of rides.
The total cost will equal _____ plus _____ times the number of rides.
Describe how to find the cost using symbols only!
Use Y to equal the total cost and X to equal the
number of rides.
Y
= _____ + _____X
Now use the graphing calculator to see the graphs of the equations that
you have written.
Press [Y=] and type in your equation for Plan A next to Y1 =.
Press [ENTER] and type in your Plan B equation next to Y2 =.
Press [ZOOM] 6 to see the graphs of the equations.
Press [ZOOM] 8 [ENTER] to see the equations in an integer window.
Now press [TRACE] and use the arrow keys to trace along the equations.
The left and right arrow keys trace along a graph and the up and down
arrow keys change the graph that is being traced. If you do not see
and equation at the top left corner of the screen, press [2nd] [ZOOM],
highlight ExprOn, and press [ENTER]. Press [GRAPH] to see the lines.
The equation tells you which graph you are currently tracing, Plan A
is Y1 and Plan B is Y2.
Trace along the appropriate line and answer the following questions
using your graphs.
- If I ride 9 rides under Plan A, it will cost ______ .
- If I ride 9 rides under Plan B, it will cost ______ .
- If I ride 30 rides under Plan A, it will cost ______ .
- If I ride 30 rides under Plan B, it will cost ______ .
- If I spent $15 under plan A, how many rides did I ride? _______
- If I spent $20 under plan B, how many rides did I ride? _______
- When would it cost the same under both plans?
________________________________________________________________________________
- Explain what you see on the graph that shows you this.
________________________________________________________________________________
- When would it cost more under Plan A?
________________________________________________________________________________
- Explain what you see on the graph that helps you to determine
this.
________________________________________________________________________________
________________________________________________________________________________
- When would it cost less under Plan A?
________________________________________________________________________________
- Explain what you see on the graph that helps you to determine
this.
________________________________________________________________________________
________________________________________________________________________________
- Comparing the graphs of Plan A and B, which of the lines is steeper
and what does this mean as it relates to the total cost?
________________________________________________________________________________
________________________________________________________________________________
- Predict what the line would look like if you graphed the following
situations:
- a plan that has no admission price and each ride is
$3.00
____________________________________________________________________________
____________________________________________________________________________
- a plan that has $25 admission price and no charge for the
rides
____________________________________________________________________________
____________________________________________________________________________
- a plan that has $5 admission price for 3 free rides, then
$1 for each additional ride
____________________________________________________________________________
____________________________________________________________________________
As a result of this activity,
students will learn how a system of equations can be used to find
the best use of information to make decisions in real world situations.
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